Expression of type Conditional

from the theory of proveit.logic.booleans.conjunction

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import B, Conditional, m, n
from proveit.core_expr_types import A_1_to_m, C_1_to_n
from proveit.logic import And, Forall, InSet
from proveit.numbers import Natural

# build up the expression from sub-expressions
sub_expr1 = [A_1_to_m, B, C_1_to_n]
expr = Conditional(Forall(instance_param_or_params = sub_expr1, instance_expr = B, conditions = sub_expr1), And(InSet(m, Natural), InSet(n, Natural)))

expr:

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\forall_{A_{1}, A_{2}, \ldots, A_{m}, B, C_{1}, C_{2}, \ldots, C_{n}~|~A_{1}, A_{2}, \ldots, A_{m}, B,C_{1}, C_{2}, \ldots, C_{n}}~B \textrm{ if } m \in \mathbb{N} ,  n \in \mathbb{N}\right..

stored_expr.style_options()

name	description	default	current value	related methods
condition_delimiter	'comma' or 'and'	comma	comma	('with_comma_delimiter', 'with_conjunction_delimiter')

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	Conditional	value: 1 condition: 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 15 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameters: 16 body: 9
7	Operation	operator: 11 operands: 10
8	Operation	operator: 11 operands: 12
9	Conditional	value: 18 condition: 13
10	ExprTuple	21, 14
11	Literal
12	ExprTuple	24, 14
13	Operation	operator: 15 operands: 16
14	Literal
15	Literal
16	ExprTuple	17, 18, 19
17	ExprRange	lambda_map: 20 start_index: 23 end_index: 21
18	Variable
19	ExprRange	lambda_map: 22 start_index: 23 end_index: 24
20	Lambda	parameter: 30 body: 25
21	Variable
22	Lambda	parameter: 30 body: 26
23	Literal
24	Variable
25	IndexedVar	variable: 27 index: 30
26	IndexedVar	variable: 28 index: 30
27	Variable
28	Variable
29	ExprTuple	30
30	Variable